Development of hypersonic aircraft demands relativistic electromagnetic scattering modeling of a high-speed moving dielectric coated object, which is applied to the recognition and tracking of moving stealth object. However, far-zone polarized scatterings from a moving 3D dielectric coated object have not been investigated so far. This paper addresses this problem by combining the finite-difference time-domain method with Lorentz transformation (Lorentz-FDTD). Through Lorentz transformation and the principle of phase invariance, the frequency, propagation direction, magnitude of the incident plane wave and the size of the moving object in the laboratory frame, which is stationary with respect to the free space, are transformed to those in the rest frame that moves with the moving object. The scattered field near the object is solved by the FDTD method with full permittivity and conductivity tensors in the rest frame, then farzone polarized scattered field is obtained by the implementation of near-to-far field transformation. Through Lorentz transformation for coordinates, the polarized Radar Cross Sections (RCSs) of moving plasma coated objects are solved. Especially, the scattering characteristics of radial radar cross sections of moving objects are discussed. Several numerical experiments are carried out, the efficiency and the accuracy of the proposed method are validated. INDEX TERMS Finite-difference time domain (FDTD), Lorentz-transformation, high-speed, anisotropic media.